We consider a problem of global regulation of a chain of integrators that has an unknown time-varying delay in the input. In contrast to the previous works in the literature, the upper bound of delay is not known. Moreover, there is no given information on the time-varying rate of delay, either. Using the dynamic gain approach inspired by the method in  and the control structure of  together, we construct an adaptive output feedback controller to solve the considered control problem. The only requirement is that the time-varying delay is bounded.